U.S. patent number 4,472,785 [Application Number 06/311,095] was granted by the patent office on 1984-09-18 for sampling frequency converter.
This patent grant is currently assigned to Victor Company of Japan, Ltd.. Invention is credited to Masao Kasuga.
United States Patent |
4,472,785 |
Kasuga |
September 18, 1984 |
Sampling frequency converter
Abstract
A sampling frequency converter for converting a first signal
sampled at a first sampling frequency f1 into a second signal
sampled at a second sampling frequency f2 comprising an
interpolation device supplied with the first signal, for inserting
L-1 zeros (L is an integer) for every sampling time, a filter
circuit for attenuating a frequency component over a frequency f/2
(f is a frequency) within an output signal of said interpolation
device, where the filter circuit has a series circuit consisting of
a finite impulse response digital filter and an infinite impulse
response digital filter, and the frequency f is equal to the first
sampling frequency f1 when f1<f2 and equal to the second
sampling frequency f2 when f1>f2, and a decimation device for
extracting every M-th (M is an integer) output signal of the filter
circuit, to produce said second signal.
Inventors: |
Kasuga; Masao (Sagamihara,
JP) |
Assignee: |
Victor Company of Japan, Ltd.
(Yokohama, JP)
|
Family
ID: |
26474655 |
Appl.
No.: |
06/311,095 |
Filed: |
October 13, 1981 |
Foreign Application Priority Data
|
|
|
|
|
Oct 13, 1980 [JP] |
|
|
55-142750 |
Nov 4, 1980 [JP] |
|
|
55-154872 |
|
Current U.S.
Class: |
708/270; 327/113;
708/313 |
Current CPC
Class: |
H03H
17/0685 (20130101); H03H 17/0288 (20130101) |
Current International
Class: |
H03H
17/06 (20060101); G06F 001/00 () |
Field of
Search: |
;364/718,723,724,328 |
References Cited
[Referenced By]
U.S. Patent Documents
|
|
|
3997772 |
December 1976 |
Crochiere et al. |
|
Primary Examiner: Shaw; Gareth D.
Assistant Examiner: Wiens; Tim A.
Attorney, Agent or Firm: Ladas & Parry
Claims
What is claimed is:
1. A sampling frequency converter for converting a first signal
sampled at a first sampling frequency f1 into a second signal
sampled at a second sampling frequency f2, said second sampling
frequency f2 being equal to L/M times said first sampling frequency
f1, where L and M are natural numbers satisfying L.noteq.M, said
sampling frequency converter comprising:
an interpolation device supplied with said first signal as an input
signal thereof, for inserting L-1 zeros for every sampling
time;
a filter circuit supplied with an output signal of said
interpolation device as an input signal thereof, for attenuating a
frequency component over a frequency f/2 within an output signal of
said interpolation device, where f is a frequency, said filter
circuit comprising a series circuit which includes a finite impulse
response digital filter and an infinite impulse response digital
filter which is coupled in series to an output stage of said finite
impulse response digital filter, said frequency f being equal to
said first sampling frequency f1 under a condition f1<f2 and
being equal to said second sampling frequency f.sub.2 under a
condition f1>f2; and
a decimation device supplied with an output signal of said filter
circuit as an input signal thereof, for extracting sampled values
in the output signal of said filter circuit at a rate of one
sampled value for every M sampled values in the output signal of
said filter circuit, to produce said second signal.
2. A sampling frequency converter as claimed in claim 1 in which
said infinite impulse response digital filter is a digital filter
described by a transfer function ##EQU12## satisfying an equation
f1L=Mf2=i.sub.p Kf2 (or i.sub.p k=M) where K is a natural number,
i.sub.p is a prime number, and a.sub.0, a.sub.1, a.sub.2, b.sub.1,
and b.sub.2 are coefficients.
3. A sampling frequency converter as claimed in claim 1 in which
said filter circuit comprises a plurality of finite impulse
response digital filters and a plurality of infinite impulse
response digital filters which are coupled in series.
4. A sampling frequency converter as claimed in claim 1 in which
the order of said infinite impulse response digital filter within
said filter circuit is selected to four or six according to the
value of M.
5. A sampling frequency converter as claimed in claim 1 in which
said infinite impulse response digital filter has an amplitude
characteristic in which an upper limit frequency of a passband
thereof is in a vicinity of a roll-off frequency due to resonance,
and has a phase characteristic which is substantially linear in the
passband thereof, and said finite impulse response digital filter
has an amplitude characteristic for cancelling a peak which is in
the vicinity of the roll-off frequency in the amplitude
characteristic of said infinite impulse response digital filter.
Description
BACKGROUND OF THE INVENTION
The present invention generally relates to sampling frequency
converters, and more particularly to a sampling frequency converter
capable of converting (hereinafter referred to as a sampling
frequency conversion) a first signal sampled at a first sampling
frequency into a second signal sampled at a second sampling
frequency.
In order to record a signal from a device operating at a
predetermined sampling frequency with an apparatus for recording
and reproducing a digital signal sampled at a sampling frequency
different from the predetermined sampling frequency, a sampling
frequency converter is used to convert the sampling frequency of
the signal which is to be recorded, so that the sampling frequency
of the signal which is to be recorded becomes equal to the sampling
frequency of the recording and reproducing apparatus. Generally,
the sampling frequency converter consists of an interpolation
device supplied with an input signal, a filter supplied with the
output of the interpolation device, and a decimation device
supplied with the output of the filter.
For example, an input signal x.sub.n at a time nT which is sampled
at a first sampling frequency f1 (where T indicates the sampling
time, and n is an integer), is inserted with L-1 zeros (L is an
integer greater than or equal to 1) at the above interpolation
device. Accordingly, a signal w.sub.nL+i is produced from the
interpolation device. This signal w.sub.nL+i can be described by an
equation ##EQU1## Hence, a frequency spectrum of the above signal
w.sub.nL+i obtained from the interpolation device becomes a
frequency spectrum in which a frequency spectrum part up to a
frequency f1/2 is symmetrically folded and distributed up to a
frequency Lf1/2.
In order to extract the output signal w.sub.nL+i of the
interpolation device at the decimation device in a manner such that
every M-th (M is an integer greater than or equal to unity) signal
is extracted and the signal is converted into a signal sampled at a
second sampling frequency f2, a frequency spectrum part above the
frequency f1/2 must be eliminated in the above frequency spectrum
of the signal w.sub.nL+i. The above filter between the
interpolation device and the decimation device is provided to
eliminate this unwanted frequency spectrum part.
The signal obtained from the filter is sampled at the decimation
device such that every M-th signal is extracted. Hence, an output
signal y.sub.n sampled at the second sampling frequency f2 is thus
obtained from the above decimation device. In this case, a relation
f2/f1=L/M stands.
The above signal y.sub.n sampled at the second sampling frequency
f2 can be described by an equation ##EQU2## where N is the order of
the filter and h.sub.m is the impulse response of the filter. As
clearly seen from this equation, the above signal y.sub.n is
determined according to the performance of the filter. Thus, when
designing the filter, there is a demand for the digital filter to
have no aliasing (folding) distortion and no delay distortion.
Further, it is desirable for the digital filter to have a simple
circuit construction.
Therefore, in a case where the first sampling frequency f1 is
smaller than the second sampling frequency f2, for example, a
finite impulse response digital filter can be used as the above
filter. However, due to the level of the present technology, the
order of the filter became exceedingly high. In a case where the
conversion ratio L/M=8/7, for example, the order of the filter
became over 1,000. When the order of the filter becomes high,
errors are easily introduced during mathematical operations.
Moreover, delay distortion is easily introduced. Further, there is
a disadvantage in that the size of the apparatus becomes large
since the order of the filter is high. On the other hand, in a case
where the conversion ratio is a small value such as L/M=1007/1001,
for example, there were cases where a filter having a
characteristic in which the passing band is one-half the frequency
band of the sampling frequency for obtaining the maximum output,
could not be realized. In addition, the order of the filter is
reduced compared to the conventional filter when a so-called
two-stage finite impulse response filter is used. However, there is
still a limit to the extent the order of the filter can be reduced,
and the order of the filter could not be reduced significantly.
On the other hand, in a case where the first sampling frequency f1
is larger than the second sampling frequency f2, for example, an
infinite impulse response digital filter can be used. When the
infinite impulse response digital filter is used to subject the
signal to a decimation process, an output having a multiplication
factor of 1/M was required as a result, for the sampled values
extracted from every M-th signal. Accordingly, transfer functions
of high order were required in both the numerator and the
denominator of the transfer function equation describing the
digital filter.
SUMMARY OF THE INVENTION
Accordingly, it is a general object of the present invention to
provide a novel and useful sampling frequency converter in which
the above described disadvantages have been overcome.
Another and more specific object of the present invention is to
provide a sampling frequency converter capable of converting a
sampling frequency with high quality, by providing a filter having
a predetermined construction between an interpolation device and a
decimation device.
Still another object of the present invention is to provide a
sampling frequency converter in which the above filter is of a low
order, and the phase distortion and aliasing (folding) distortion
introduced when a signal recorded with a first sampling frequency
is reproduced with a second sampling frequency, can be eliminated.
According to the sampling frequency converter of the present
invention, errors introduced during mathematical operations can be
greatly reduced, since the order of the filter is low.
Other objects and further features of the present invention will be
apparent from the following detailed description when read in
conjunction with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a system block diagram showing an embodiment of a
sampling frequency converter according to the present
invention;
FIG. 2 is a diagram showing a frequency spectrum of an output
signal from a part of the block system shown in FIG. 1;
FIG. 3 is a diagram showing frequency characteristics of a finite
impulse response digital filter and an infinite impulse response
digital filter;
FIG. 4 is a diagram showing a filter characteristic of an example
of an infinite impulse response digital filter;
FIGS. 5A and 5B are diagrams respectively showing a total frequency
characteristic of a filter in the block system shown in FIG. 1;
FIG. 6 is a diagram comparing filter characteristics of a
conventional filter and a filter according to the present
invention;
FIGS. 7A and 7B are diagrams respectively showing a frequency
characteristic of an infinite impulse response digital filter;
FIG. 8 is a diagram showing a total frequency characteristic of a
digital filter; and
FIGS. 9A and 9B are diagrams respectively showing a frequency
characteristic of a digital filter within a sampling frequency
converter according to the present invention.
DETAILED DESCRIPTION
In FIG. 1, an input signal x.sub.n supplied to an input terminal 10
is supplied to an interpolation device 11. The above input signal
x.sub.n is a signal at a time nT (n is an integer), where T is the
sampling time, obtained by sampling a signal at a first sampling
frequency f1. The input signal x.sub.n thus supplied to the
interpolation device 11 is inserted with L-1 zeros (L is an integer
greater than or equal to 1), and converted into a signal w.sub.nL+i
which can be described by equation (1). ##EQU3## Accordingly, the
frequency spectrum of the above signal w.sub.nL+i becomes as
indicated in FIG. 2. That is, the frequency spectrum of the signal
w.sub.nL+i becomes a frequency spectrum indicated by a solid line
in FIG. 2 wherein the frequency spectrum of the input signal
x.sub.n indicated by a part with oblique lines is symmetrically
folded and distributed up to a frequency Lf1/2.
Every M-th (M is an integer greater than or equal to 1) output
signal w.sub.nL+i from the interpolation device 11 is extracted at
a decimation device 17 which will be described hereinafter.
However, in order to obtain the signal w.sub.nL+i as a signal
sampled at a second sampling frequency f2 (f1<f2, for example),
the frequency spectrum part other than the part indicated by the
oblique lines in FIG. 2, that is, the frequency spectrum part over
the frequency f1/2, must be eliminated. Accordingly, a filter 13
provided between the interpolation device and the decimation device
having a lowpass digital filter characteristic, for example, is
used in order to eliminate the above frequency spectrum part other
than the part indicated by the oblique lines.
Every M-th signal obtained from the above filter 13 is sampled and
extracted by the decimation device 17, and converted into a signal
v.sub.n which is sampled at the second sampling frequency f2. This
signal v.sub.n is produced through an output terminal 18. In this
case, a relation f2/f1=L/M stands.
The sampling frequency is thus converted from the first sampling
frequency f1 to the second sampling frequency f2. The above signal
v.sub.n which is sampled at the second sampling frequency and
produced through the terminal 18 can be described by equation (2).
In equation (2), N is an integer indicating the order of the filter
13, and h.sub.m indicates the impulse response of the filter 13.
##EQU4##
As clearly seen from the above equation (2), the signal v.sub.n is
determined according to the performance of the filter 13.
Accordingly, when designing the filter 13, care must be taken so
that aliasing (folding) distortion and delay distortion are not
introduced. Further, it is desirable to design a filter having a
simple circuit construction.
However, as described, when the above filter 13 is constructed from
a finite impulse response (FIR) digital filter in a case where the
first sampling frequency f1 is smaller than the second sampling
frequency, for example, the order of the filter became exceedingly
high. Moreover, when an infinite impulse response (IIR) digital
filter is used to construct the filter 13 in a case where the first
sampling frequency f1 is larger than the second sampling frequency
f2, for example, the order in the numerator and the denominator of
the transfer function equation describing the IIR digital filter
became exceedingly high.
Therefore, in the present invention, the above filter 13 is
constructed from a combination of the FIR digital filter and the
IIR digital filter, in order to eliminate the above described
problems.
In the present embodiment of the invention, the above filter 13
consists of an FIR digital filter 14 provided with the output
signal of the interpolation device through a terminal 12, and an
IIR digital filter 15 supplied with an output signal of the FIR
digital filter 14. An output signal of the above IIR digital filter
15 is supplied to the decimation device 17 through a terminal
16.
In the present embodiment, the IIR digital filter 15 is coupled to
the output stage of the FIR digital filter 14 as shown in FIG. 1,
for the following reasons. That is, the word length of the
coefficients in the transfer function of a digital filter in
general, is limited for these coefficients to be processed
digitally. Thus, it is desirable that the word length of the
coefficients is short. Generally, the IIR digital filter 15 is
constituted by a recursive digital filter. For this reason, the
word length of the coefficients in the transfer function of the IIR
digital filter 15, becomes longer compared to the word length of
the coefficients in the transfer function of the FIR digital filter
14. If the IIR digital filter 15 is coupled to the input stage of
the FIR digital filter 14, the word length employed in the FIR
digital filter 14 inevitably becomes long. Therefore, it is
preferable not to couple the IIR digital filter 15 to the input
stage of the FIR digital filter 14. Further, as will be described
later on in the specification, the IIR digital filter 15 is
designed to have a resonance point in the vicinity of an upper
limit frequency of the passband, so that the phase characteristic
thereof becomes substantially linear (flat) at least in the
vicinity of the passband. Accordingly, if the IIR digital filter 15
is coupled to the input stage of the FIR digital filter 14, an
overflow may occur during the operational processing in the FIR
digital filter 14 at a frequency in the vicinity of the resonance
point frequency of the peak in the amplitude characteristic of the
IIR digital filter 15. It is for these reasons that the FIR digital
filter 14 is coupled to the input stage of the IIR digital filter
15.
The FIR digital filter 14 is generally a nonrecursive digital
filter described by a difference equation (3). In equation (3), N
is an integer indicating the order of the filter, a.sub.i is a
coefficient, x.sub.n is the input signal, and y.sub.n indicates the
output signal. ##EQU5## The frequency characteristic of the above
FIR digital filter 14 is indicated by a dotted line I in FIG. 3. As
indicated in FIG. 3, a frequency F.sub.p1 at the end of the passing
band of the frequency characteristic is lower than the frequency
f1/2 which is one-half of the first sampling frequency f1, and a
frequency F.sub.s1 at the end of the attenuation band is selected
to a frequency slightly higher than the frequency f1/2. Thus, the
FIR digital filter 14 has a lowpass filter characteristic.
On the other hand, the frequency characteristic of the above IIR
digital filter 15 is indicated by a solid line II in FIG. 3. This
frequency characteristic is a characteristic in which the end of
the passing band is selected at a frequency F.sub.p, and the end of
the attenuation band is selected at a frequency F.sub.x (where
F.sub.s >F.sub.p) which is slightly lower than the frequency
f1/2.
A filter of the following construction, for example, can be used as
the above IIR digital filter 15. First a resonance circuit having
an impedance Z(s), a resonance angular frequency .omega..sub.o,
quality factor Q, and the like given by equation (5), is expanded
into the numerator and the denominator. ##EQU6## Moreover, a
transfer function H(s) of the Laplace transformation form is
defined by equation (6). ##STR1## In the above equation (6),
s.sub.i1 and s.sub.i1 indicate poles, s.sub.i2 and s.sub.i2
indicate zeros, and N.sub.o is the order of the filter.
Accordingly, a transfer function H.sub.z (z.sup.-1) of the digital
filter defined by equation (7) is obtained by use of matched
z-transform. ##EQU7## In the above equation (7), the term A.sub.i0
is defined by equation (8). In equation (8), .omega..sub.N
indicates the normalizing angular frequency, and T.sub.o is the
sampling time of the input digital signal. ##EQU8##
When obtaining an amplitude versus frequency characteristic which
indicates attenuation at a range between desired angular
frequencies .omega.1 and .omega.2 (where .omega.1<.omega.2), the
terms f(r.sub.i1, .theta..sub.i1) and f(r.sub.i2,.theta..sub.i2) in
the above equation (6) describing the poles s.sub.i1 and s.sub.i1
and the zeros s.sub.i2 and s.sub.i2 are substituted by the angular
frequencies .omega.1 and .omega.2. Furthermore, in the case where
the order N.sub.o of the filter is an even number, the above
.theta..sub.i1 and .theta..sub.i2 are respectively set to .pi./2.
On the other hand, in the case where the order N.sub.o of the
filter is an odd number, a pair of poles and one zero are
positioned on the real-axis on the s-plane.
In addition, when obtaining an amplitude versus frequency
characteristic which indicates intensification at the range between
the angular frequencies .omega.1 and .omega.2, the angular
frequencies .omega.1 and .omega.2 are substituted into the
equations describing the poles s.sub.i1 and s.sub.i1 and the zeros
s.sub.i2 and s.sub.i2 in the above equation (6).
In the above example of the IIR digital filter, it has been
confirmed that the linear part in the passband of the phase
characteristic is increased when the values of the above
.theta..sub.i1 and .theta..sub.i2 are respectively set to
89.5.degree. and 89.9.degree..
The IIR digital filter 15 is generally a recursive digital filter
described by a difference equation (9). In equation (9), p.sub.n is
the output digital signal at the time nT, y.sub.n is the input
digital signal at the time nT, and a.sub.0 through a.sub.2,
b.sub.1, and b.sub.2 respectively are coefficients.
However, when the ratio L/M in the IIR digital filter defined by
the above equation (9) becomes large, the value before the
decimation operation is performed must all be calculated with
respect to each output digital signal p.sub.n, when the filter is
designed.
Therefore, in the present embodiment of the invention, the
following designing method is used. First, a transfer function
H(z.sup.-1) of the IIR digital filter 15 in the z-region is defined
by equation (10). ##EQU9##
In the digital filter defined by the above equation (10), the
following relationship exists between the first and second sampling
frequencies.
In equation (11), K is an integer, and i.sub.p is an arbitraty
prime number (i.sub.p =1, 2, 3, 5, - - - ).
When the term "z.sup.-1 " in equation (10) is substituted by a term
"z.sup.-k ", a following equation (12) can be obtained. ##EQU10##
When the above equation (12) is written in the form of the
difference equation (9), a following equation (13) is obtained.
FIG. 4 indicates the frequency characteristic of an example of an
IIR digital filter described by the above equation (13). In this
example, a fold is generated as indicated by a, however, the
frequency characteristic indicated by the solid line II in FIG. 3
can still be obtained.
In a case where i.sub.p =2, the apparent order of the filter
described by the equation (13) is "2". However, since a relation
2K=M can be obtained from the equation (11), it is clear that the
equation (13) is multiplied by two. Accordingly, the actual order
of the IIR digital filter 15 becomes "4" regardless of the value of
M. For example, when the value of M is 526, the order of the
mathematical operation performed with respect to the denominator in
the equation (12) in a normal IIR digital filter, that is, the
order of the recursive term becomes 526.times.2=1052. However, in
the present embodiment of the invention, the order of the IIR
digital filter 15 having every M/2-th sampling value as the input
and output, is only "4".
The frequency range where the above fold indicated by a in FIG. 4
exists, is within the attenuation frequency range of the FIR
digital filter 14. Accordingly, by providing sufficient attenuation
quantity, the effects due to the above fold (aliasing distortion,
or folding distortion) can be eliminated. Therefore, in the present
embodiment of the invention, the signal supplied to the terminal 12
is given a frequency characteristic indicated in FIGS. 5A and 5B.
Hence, the signal which has passed through the filter 13 is
produced through the terminal 16 as a signal having only the
frequency spectrum part indicated by the oblique lines in FIG.
2.
According to the experimental results obtained by the present
inventor, in a case where the conventional FIR digital filter is
used as the filter 13 under a condition M=2, L=1, f1=47.25 kHz,
f2=94.5 kHz, F.sub.p =20 kHz, and F.sub.s =22 kHz, the order of the
digital filter becomes "224", and the frequency characteristic of
the digital filter becomes as indicated by a solid line in FIG. 6.
On the other hand, according to the present embodiment of the
invention, the order of the FIR digital filter 14 is "51" and the
order of the IIR digital filter 15 is "4", and the order of the
filter 13 as a whole becomes "55" which is an exceedingly low
order. Thus, a desired frequency characteristic indicated by a
dotted line in FIG. 6 can accordingly be obtained by the filter 13.
In this case, the coefficients a.sub.0 through a.sub.2, b.sub.1,
and b.sub.2 can respectively be obtained as follows. ##EQU11##
Moreover, the impulse response of the IFR digital filter 14 having
the order of "51" becomes as follows. In the equation (13), a.sub.i
=H(i).
______________________________________ H(1) = 0.29722860E -5 =
H(51) H(2) = 0.68821300E -4 = H(50) H(3) = 0.24645380E -3 = H(49)
H(4) = 0.32557170E -3 = H(48) H(5) = -0.10708640E -3 = H(47) H(6) =
-0.91904700E -3 = H(46) H(7) = -0.91756040E -3 = H(45) H(8) =
0.84177960E -3 = H(44) H(9) = 0.27545770E -2 = H(43) H(10) =
0.13450910E -2 = H(42) H(11) = -0.36163680E -2 = H(41) H(12) =
-0.59536470E -2 = H(40) H(13) = 0.38218610E -3 = H(39) H(14) =
0.10232020E -1 = H(38) H(15) = 0.88977400E -2 = H(37) H(16) =
-0.81775670E -2 = H(36) H(17) = -0.21448790E -1 = H(35) H(18) =
-0.64911810E -2 = H(34) H(19) = 0.27803460E -1 = H(33) H(20) =
0.35338160E - 1 = H(32) H(21) = -0.12793650E -1 = H(31) H(22) =
-0.71780800E -1 = H(30) H(23) - -0.47199580E -1 = H(29) H(24) =
0.10264440E 0 = H(28) H(25) = 0.29608490E 0 = H(27) H(26) =
0.38523240E 0 = H(26) ______________________________________
In FIG. 6, attenuation quantities of -81 dB and -84 dB are
respectively obtained at frequencies of 23 kHz and 24 kHz, in the
conventional example. On the other hand, according to the present
embodiment of the invention, attenuation quantities of -70 dB and
-105 dB are respectively obtained at frequencies of 23 kHz and 24
kHz.
In addition, in a case where i.sub.p =3, that is, when 3K=M, the
order of the IIR digital filter 15 becomes "6" since the equation
(13) is multiplied by three (since the IIR digital filter 15 has
every M/3-th sampling value as input and output in this case).
Similarly, in a case where i.sub.p =1, the order of the IIR digital
filter 15 becomes "4".
Furthermore, the IIR digital filter 15 is designed so that the
phase characteristic thereof is substantially linear (flat) at
least in the passband. In other words, the amplitude characteristic
of the IIR digital filter 15 is selected to a characteristic shown
in FIG. 7A and indicated by a broken line IIR in FIG. 8. In this
amplitude characteristic of the IIR digital filter 15, there is a
peak due to resonance in the vicinity of an upper limit frequency
(cut-off frequency) f.sub.c of the passband, and there is a dip at
a frequency f.sub.o. Accordingly, the roll-off frequency in the
amplitude characteristic of the IIR digital filter 15, becomes in
the vicinity of the above upper limit frequency f.sub.c. In
addition, by selecting the amplitude characteristic of the IIR
digital filter 15 to such a characteristic, the phase
characteristic of the IIR digital filter 15 becomes as shown in
FIG. 7B. As seen from FIG. 7B, the phase characteristic of the IIR
digital filter 15 is substantially linear (flat) at least under the
upper limit frequency f.sub.c.
On the other hand, the amplitude characteristic of the FIR digital
filter 14 is selected to a characteristic indicated by a broken
line FIR in FIG. 8. This amplitude characteristic of the FIR
digital filter 14 cancels the peak in the vicinity of the roll-off
frequency in the amplitude characteristic of the IIR digital filter
15. Moreover, the phase characteristic of the FIR digital filter 14
is substantially flat in the passband. Accordingly, the amplitude
characteristic of the digital filter 13 as a whole, becomes as
indicated by a solid line in FIG. 8. This amplitude characteristic
of the digial filter 13 is flat in the passband, and shows a sharp
roll-off attenuation characteristic. Further, the phase
characteristic of the digital filter 13 as a whole, is
substantially linear (flat) at least in the passband.
In the above embodiment of the invention, the relationship between
the first and second sampling frequencies f1 and f2 was assumed to
be f1<f2. However, in a case where f1>f2, the frequency
component over the frequency f2/2 must be eliminated by the filter
13. This elimination of the frequency component is performed in
order to eliminate the unwanted fold frequency component over the
frequency f2/2 in advance.
The digital filter 13 consisting of the above described FIR digital
filter 14 and the IIR digital filter 15 has a total frequency
characteristic indicated by a solid line in FIG. 8 and FIGS. 9A and
9B.
Accordingly, when the conversion ratio f1/f2 between the first and
second sampling frequencies f1 and f2 respectively are 14/15 and
21/20, the order, the multiplication number, and the ratio with
respect to the multiplication number of the filter according to the
present invention, respectively become as indicated by following
Tables 1 and 2. Table 1 indicates a case wherein the sampling
frequency is converted from 44.1 kHz into 47.25 kHz (f1<f2). On
the other hand, Table 2 indicates a case wherein the sampling
frequency is converted from 50.0 kHz into 48.0 kHz (f1>f2).
TABLE 1
__________________________________________________________________________
FIR DIGITAL FILTER CONVERSION DIGITAL 2-STAGE FIR OF PRESENT RATIO
FILTER DIGITAL FILTER INVENTION
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14/15 ORDER OF FILTER 1563 1.62.about.2,210 1.723.about.2.2
MULTIPLICATION 111.6 214.4 71.6 NUMBER RATIO 1.56 2.99 1
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TABLE 2
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FIR DIGITAL FILTER CONVERSION DIGITAL 2-STAGE FIR OF PRESENT RATIO
FILTER DIGITAL FILTER INVENTION
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21/20 ORDER OF FILTER 2381 1.47.about.2.341 1.1107.about.2.2
MULTIPLICATION 344.4 109.1 NUMBER RATIO 3.16 1
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Moreover, a characteristic similar to that described above can also
be obtained by use of a filter in which a combination consisting of
a plurality of FIR digital filters 14 and IIR digital filters 15
are respectively connected in series.
Further, the present invention is not limited to these embodiments,
but various variations and modifications may be made without
departing from the scope of the present invention.
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